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AP EAMCET2001MathematicsDifferential Equations

The solution of x d x+y d y=x^2 y d y-x y^2 d x is

Options

  1. Ax^2-1=C (1+y^2 )
  2. Bx^2+1=C (1-y^2 )
  3. Cx^2-1=C (1-y^2 )
  4. Dx^2+1=C (1-y^2 )

Correct answer

A. x^2-1=C (1+y^2 )

Step-by-step solution

We have, aligned x d x+y d y & =x^2 y d y-x y^2 d x x d x+x y^2 d x & =x^2 y d y-y d y (1+y^2 ) x d x & =- (1-x^2 ) y d y aligned On integrating both sides, aligned 2 x d x -1+x^2 & = 2 y d y 1+y^2 (-1+x^2 ) & = (1+y^2 )+ c x^2-1 & =C (1+y^2 ) aligned

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